A bicycle odometer (which measures distance trapz 7ohvm+boj):.d 4kiq; 1amwveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with7vawhm;o z)jkp+om 4b .1 :diq 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pr 740g xyob5xzoint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration chazxoy bg0r5x4 7nge?

Could a nonrigid body be described by a single 1by 0i2 gq0wwkqn2f bg 5dtm((value of the angular velocity $\omega$ Explain.

Can a small force ever owdobz4vb+4dt .uq 84exert a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head than s-5w7+q8 w wk09aqf+l esklazwhen your arms are stretched out in front +slsww -9 f75k al0qwe8a+q zkof you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three a z5mld4m3yd;fjfg2 + gen9k2st the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is 3 + fkmge52n9fjsz; 4gd 2ylmdit harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on be5op;m)i)she) g95d u gnkqgn7ing able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantaggqmg )h59 )5kn ;uds)epgo7nieous.

Why do tightrope walkers (Fig. 8–35) carry a lon8 bznn zx()l5ng, narrow beam?

If the net force on a system is zero, is the net torque also zero? If t8 i3hesmrh: mj:b y/;ohe net tos:hioy3j8b h;/mm :rerque on a system is zero, is the net force zero?

Two inclines have the same height e8yq6m0zpy)l3 6wkfb but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline6)pk638ly y ewqzfm b0 will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incjs6cm jd k7cxw,d 3z/*kihfm60 )p rk,line. One spherermkk66wkcj xfpm /h,zs3d,) j07*c di has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and thzf0m7ma0yz)/o h:w.bv ( t jijpl;a .re same mass. They start from rest at the toprl z ih mj/vb0ya.j)p:07oawt .f (;mz of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or ruj-x8 ,nkz kd yfw. :ehfo/tmw/ v:nx:,lw4(jotating objects eventually u:w:exn(vltk8 w/f: nk,jd j4m- xf y/ho.z,wslow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how would sf:naokmx- 9 yu.9;xithis affect the lengthu9kxsom -n:y9 a .xif; of the day?

Can the diver of Fig. 8–29 do a somersaulth k+gx yn3w*ylpx0j- + without having any initial rotation when she leaves t+0hyx g+l wyj3 p-xkn*he board?

The moment of inertia of a rotating solid disk abt3trnva*box1y h*n s,8hc -2wout an axis through its center o ah,ntc2 sxt w1ob*h3-r vn8*yf mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotatingym c,,un +s5wb stool holding a 2-kg mass in each outstretched hand. If you suddenly drop th ,w+,cymbsun5 e masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical aw7 -i*l5ypw dec3 8l4xkf-x-fc ;v rwzw2md:xnd have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine8xk2x;-wml3wrzy*7-c i:- v5plfwd4c fd x we which is which.

The angular velocity of a wxtbu 1pmn*-s1 heel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential li1 sp* ux-mt1bnnear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing oac-yk w/+zp:qhy9ck; n the edge of a large freely rotating turntable. What hah+y /kpa:;zk-wc yq c9ppens if you walk toward the center?

A shortstop may leap into the air to catch a b-2wisq 7vih /cl- mo:7 ygvg1oall and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly yo m-i7 glv1woh:7c v-i2 ys/oqgu will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum7jh8mq1v;fpp , discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelp7f;p vhj8 q1mler can operate to keep the helicopter stable.

  Express the following angles in radians: (a9rl(h 3 s :d37 e*bgh+xrbkpfy) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, usitbaezyeqsk.m+2a cd/e7( y4 5ng the info(yt2e.7az sm4/ae+ y dkeq5cbrmation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km+caqxk-en 2/sj o)xk/ from Earth. The beam diverges at an aa/jkkn ) cxeq-2xs/o+ ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mot9k,tu;alrblgt/ ( h ;hor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular ar;9;lb h /tktl,(g haucceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another childjhp40h0/ xsuirp, 2r, atgsq 3. If the ball makes 15.0 revo j2h su0rphx0,qgp, sia/t43 rlutions, what is its diameter?    m

  A bicycle with tires 68 cm i si -/j11ztptgp2 2 iygm8onc4n diameter travels 8.0 km. How many revolutions do the wheels make? pctoi/-zgn pg4m 2 ty8 112jis   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcuuer)91 yjr :kulate its angular velocity in :) 1yeu jk9urr$rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38x/5wd da2 ba*t+i2kfip6ne-p ). (a) What is the linear speed of a chilixk ti/6bdfp2 - 5a*an2 dpe+wd seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of t/q2-j5 6u t xou+wv qk 37wlnvmv+c:uohe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a p 7gdzp .f( y9pi)+p))hk(soggz r(tz boint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axi ,bmtlm px101is of rotation is to experience an accele01plbt m ,imx1ration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13eu-m nmtc.k4q+vdm/6 0 rpm to 280 rpm in 4.0 smm -/c n64+d.ke umqtv. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu5/-refy +;g . e-vv0rb(vtm:ip 5tzl jlm 7wcxs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft imx(j )*l,btn put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution ev ( xm)itln*j,bery minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 22ukdsa4. 6i0l4wn y z)e0 s. Through how many revolutions did it turn sz)4ai0n duew.l 6yk4in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpmy1ia-rxo;s)u5m.x+ j /gjs jh in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspqg 6dgd:3 ha1rvz6jm1eed jets in a whirling “human centrifuge,” which takes 1.0 min to turn tavqj 1 h:ddz6g3gm16rhrough 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates ulq)tybbw s9/ 8niformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have 89w/tbq b )lystraveled in this time?    m

  A cooling fan is turned off when it is running at w2 fs4 y48 bnamrwi2nywo;d87850rev/min It turns 1500 revolutions before it comes to arywfboaw4; 8 n 2y28wn4idm7s stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the caa 9.dpces4ngs z 9 -r01ysx(l+jk: xcpr reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.p1.zds( 99nk-jap 0yg c:slxcxse+r 4
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces it z2njlds6mw a,v g+ps9xk /o4nl-nn2 9s speed uniformly from 95km/h to 45km/h The tires have a x+, g 6s 29/9jvnnpdwzn ak-2os lnml4diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her wei,duec/av ;pxs91 j kr/o znov25iuuem20u 0 6lght on each pedal when climbing a hill. The pedals rotate in a circlu ;/es,zu51jokp u2vxoac029umrd 0 ni/l6ev e of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm 59rpx )t :3w hwf.kyw4eo4 nfhwide. What is the magnitude of the torque if the force is fw 4t5 k:p4owwneh.rhf39)xy exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about thei3s;yyx8zk6 5vuqpa 1 hd5o 8e axle of the wheel shown in Fig. 8–39. Assume that a friction torq;uk6s5ia3y8ev8z15 yxoh p dque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mi- +ruz rdkyja +4+eqbv-0/pr assless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the+-b+ /rkpuzi r +e arvj4q0dy- net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a tojuj8:nfb9)f- 7qa 3r z/sklp yrque of 38r-z3l7b:fujj)9 q s np8 k/fya $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere o yy.(t4 :iii tg7g)ancf radius 0.648 m when the axis of rotation is through .(:ai )yyn7c tg4tigiits center.    $kg \cdot m^2$

  Calculate the moment oy/dn q-*- fsevj(a6hhkd b:u5f inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the:vdje kq -bf6*-hh ua n(5/syd hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontal3/r mbh44 qw gis+vb w,zbfq 83..mbeh 3 .e qm/.zm4 3hwb b+f4sqbbi,w8 grvhcircle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheeli (c+ah)r (gbu rotating at constant angular speed (Fig. 8–42). Thec( hbri)ga (u+ friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fcgbwq)p0 y (ihj;t( 1xduo;a2 ig. 8–43 abox;02wh(cqajbdg ;up1io(y) t ut
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose tot0(m,ka yr: +uhi)bhxval mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cyldw:g,ot) a 1g v7oy5qgindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of 1oq7y ga d,tg:w5g)vo each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm any+ (ind rip3q3d a mass of 0.580 kg. Calcular3ny (d+ip i3qte
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from resk- cm3n:f aqg1t to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is ablb8u 8f3ehd6 zre to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite eac86rfd8h3b zeuh other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300ru. ggury .w0: rpm is shut off and is eventually brought ug w.u.ru0:gr yniformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8– h/sl3zw09g5i rhebb;45 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forear iqfs9keqvxzqh5: +b;ai (dxv9 q0 2k*m, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from r99 dk5q0bizq h q(f ixx+a; 2vqek*:vsest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. s 1,yt qbfxd6q124gnv8–46.4 fb 1s16,v q2nqtydxg
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists o adei:m5 )ijx-f two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accexf:2pv7f3j fljo2y7d4ndzdv p9. 6 fclerates the hammer from rest within four full turns (revolpfff dc7xd lvjzfy 6p22 .d7n:43j9ovutions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inerjwyq3m;0,v sc +s5pwj tia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2lur2 lu6eo: yo0(gq3l80 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.32tuwf/r-w0 n cia3p-w kg and radius 9.0 cm rolls without slipping down a lane at-3w w /2icf-0prunatw 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enem ycvr b2viqi /3*4n,taq3. eurgy of the Earth with respect to the Sun as the sum of two terms, vn v3e/4. m2 a3tubcq,r*i qyi
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How muchy s7,;hmnj2u +il ilj, net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? yimn 2u,j+slj; ,7hliAssume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1 0,ibpm(pzv)2r: imy w.80 kg starts from rest and rolls without slp,(:wr y2ivb mz p0)miipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balance2(iyhpl)qnjt 5d)u*m 7 nweq3d vertically on its tip. It starts to fall and its lower end does not slip. What wdi)q*nh57tw(uqe 2ylmn )j3pill be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momw8gcvsc9f: i)e z3yb5entum of a 0.210-kg ball rotating on the end of a thin string in a ciczvyfc8w:3) 95geis brcle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricall ):wwg8gvc5 a2evbi) grinding wheel of radius 18 cm when rotating at 150awe5igv8v) :gb )clw 20 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is ro3 l(soz.81 ef ap3)n tlsq8 m+rcxt5kdtating at a rate of 1.3rev/s If he raises )a3 (ndtcm8t r+5f osllsexkq3p1.8zhis arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown i4le5- cr mei;gn Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s whe;e ig5cr-le4 mn in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial r.kvo1 91z0j qupv5q-ojzd i/pate of 1.0 rev every 2.q pqvz1vpd 5o91.ujo-/0ikjz0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis ,i(u)mew i0 vythrough its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diamet,ii(0e)m w vyuer 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure t7muxfr46*/ a rqh hm*qk)s n)2-qoaa skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentu 76ae )3d7ags yqve)nzm of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of *wy0v f0q s4vainertia I is dropped onto an identical disk rovwafsvy00* 4 qtating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsnuow vbq3(0 (3lz+rb x at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round plagcv zbo-mhs)7::bzcf17 ag/ptform of radius 3.0 m and moment of inertia/ h)c 7zgca:vozf1:ps7bb m -g 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freel:x fmxc7)o5 efy with an angular velocity of 0.8o7fmfe)5 x:xc $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventuallyb*bgp* yz0cewe6ttkv5860m q collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assumk*e *8vm 00q6 bcwbzt5tp 6geying the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in ex ;30lnxd3ie secess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass f7q/;pxc8 owp6cfc .t$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initial7tlh9pd jk +a.ly at rest, that can rotate freely without friction. The moment of inertia of the person pl+dt apljh9k7 .us the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person d+q n/gitc c gi4:t/u:stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of q4t: :iu/ gtg+ncic /d 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground wit4e ign7*va c8eh the end of the rope lying on the top edgcve *e 4gni78ae of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Eart* 7x8u*tq8j nh-uxk fjh such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to itux8 qu8jf7xj *thnk *-s orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/loq,eapmu z ,l )gq(l5s5m ;9x$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a 7e ejhvw z;rm j4mhms6iq)h:*;o9 4yc uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular cw4eovj;h mqjz yhi9er 4):7 m6m*sh ;acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and d5ec- bbwfk*0 zn/x+ xwiameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linea5x wx bb/+fzek* 0wcn-r speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whee4n;mbrr bp+cryy+ 2ql--wb)e l ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 tin:q4m ;ors1g-sjgk b0 mes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its maj41krn g; -smqsb go0:ss in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lowhl *0 agm9 hvln)az3l7-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppoh*vll m )7a hzl309gnase such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates*j hhoqj/1c3mhha 1p 0 an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a o l,:b2aw0(*paek j4eov 5azbwr:ws 5horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fricuwlsyt ieiw5x*9 /zt 2pwk544tion) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the w4izix4utpetw2 5k wls5 y/9 *moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. 0mzi7a h3 hcd.It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it w.id7az0 h hc3mill climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on et2qo(af o k 6b1-ylj-f6ouv9 a flat road is making a turn with a radius The forces acting on the 6u2yajkqoeb t -f9-1vl6o ( focyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and bekvn2prc:o-x.jo 6(s3pvwljc(( l7t fgins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a cp: l7f(t (jvxrj v(p3ck 6slnoo-2w.rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s //rf;h7k zcf kbody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinninkr/ 7;f/zckfhg skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platesz j3ojt*b-k ew la.) 4n+x xit0ezmal;.m ,,bm, of mass. n,jzlmxtbimx ab t*kz;jmweae 3l-)0 +.4o, $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls alon ieh5d(sf :7atg the looped rough track of Fig. 8–58. e:(ahsi7 ftd5What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but()/43ddurooq tvoxp ; y)+hyf do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ugflg sl4 4p-0nnd21ncniformly from 90km/h to 60km/h The tires have a d 410fc g2gn 4npllnds-iameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s